Initial Mean Stress Research Articles

Automating the Calibration of Flat-Jointed Bonded Particle Model Microproperties for the Rewan Sandstone Case Study

The flat joint contact model (FJM) provides significant improvements over its predecessors, the parallel bond and contact bond models, for bonded particle modelling of rocks due to its unique microstructure that allows for the reproduction of the macroscopic compressive–tensile strength ratio, σc/|σt|; internal friction angle, ϕ; and the Hoek–Brown constant, mi. However, the microproperty calibration process is tedious and time-consuming to perform manually due to the various microproperty interdependencies that exist in the FJM. Previous attempts at automating the bonded particle model microproperty calibration process have typically utilised advanced statistical methods, such as artificial neural networks, but they have not yet been widely applied to the FJM over a representative range of confining stresses for calculation of ϕ and mi. In this study, a new method is proposed for automating the FJM microproperty calibration process based on a numerical root-finding algorithm and specific calibration sequencing. The new method is applied to a Rewan Sandstone case study with similar natural porosity to a 2D bonded particle model packed to a low initial mean stress. The resulting FJM microproperties are shown to reproduce both the target macroscopic laboratory properties and a realistic damage evolution, including a normalised crack initiation stress of 0.46 and a normalised crack damage stress of 0.83 coinciding with a reversal of the axial stress–volumetric strain curve in an unconfined compression test simulation. It is also demonstrated that the absolute change in the instantaneous lateral–axial strain ratio (Poisson’s ratio in the linear-elastic phase) provides a reasonable proxy to the acoustic emissions which may be measured in the laboratory.

Drained expansion analyses of a cylindrical cavity in sands incorporating the SANISAND model with fabric change effect

Sandy soil exhibits inherently anisotropy due to its microstructure, also known as ‘fabric’. However, the drastic change in fabric observed during the dilatant phase is often overlooked in current cavity expansion research. This paper presents a drained expansion solution of a cylindrical cavity with fabric change effect in the sand using a simple non-associated and anisotropic model, SANISAND. The problem is formulated as a set of first-order differential equations with the unknown variables as functions of an auxiliary coordinate, which can be solved as an initial value problem. A subroutine is implemented into the FEM simulation to verify the proposed method. Additionally, cavity expansion solutions in sand are compared with those based on state-dependent dilatancy. The anisotropic fabric of the sand is studied to investigate the impact of the initial void ratio, initial mean stress, and at-rest coefficient on the void ratio path, stress distributions and paths, and bounding surfaces. The proposed solution provides a framework for the potential use of cavity expansion in sand, considering the fabric change effect, and a benchmark for further developments and numerical calculations by using the SANISAND model.

Behavior of Sand–Tire Chip Mixtures in Constant Shear Drained Stress Path

This paper presents the potential of scrap tire in controlling the onset of instability of sand in the constant shear drained (CSD) stress path. A series of triaxial tests in the constant shear drained stress path was conducted on the sand and sand––tire chip (STCh) mixtures. All the tests were performed following the conventional consolidated drained (CD) test up to a predefined deviator stress (onset of CSD). The CSD test then was carried out on samples at the onset of CSD by reducing the confining pressure while maintaining the deviator stress and backpressure constant. The effect of different deviator stress (qCSD), initial mean stress (po′) levels, and tire chip content (TCh) on the onset of instability were investigated. The instability of sand and sand–tire chip mixtures was determined based on the decrease in the constant deviator stress (dq<0) and second-order work criteria (d2W<0). Both approaches were found to be consistent in determining the onset of instability of STCh mixtures. The onset of instability of sand is influenced by the TCh content and qCSD. On other hand, a unique value of pf′ was found for different values of po′. The optimum performance in controlling the onset of instability of sand was found for TCh=20% for the tire chip considered in this study. The mobilized effective friction angle also exhibited improved performance for TCh = 20%. In addition, the modified state parameter had good correlation with the mobilized effective friction angle in the CSD stress path.

Evolution of granular materials under isochoric cyclic simple shearing.

By means of 3D particle dynamics simulations, we analyze the microstructure of granular materials subjected to isochoric (constant volume) cyclic shearing, which drives the system towards a liquefaction state characterized by loops of jamming-unjamming transition with periodic loss of strength and irreversible accumulation of shear strain. We first show that the macroscopic response obtained by these simulations agrees well with the most salient features of the well-known cyclic behavior of granular materials both before and after liquefaction. Then we investigate the evolution of particle connectivity, force transmission, and anisotropies of contact and force networks. The onset of liquefaction is marked by partial collapse of the force-bearing network with rapid drop of the coordination number and nonrattler fraction of particles, and significant broadening of the contact force probability density function, which begins in the preliquefaction period. We find that the jamming transition in each cycle occurs for a critical value of the coordination number that can be interpreted as the percolation threshold of the contact network and appears to be independent of the initial mean stress, void ratio, and cyclic shear amplitude. We show that upon unjamming in each cycle an isotropic loss of contacts occurs and is followed by the development of high contact anisotropy and a large proportion of particles with only two or three contacts. The higher mobility of the particles also involves a lower degree of frustration of particle rotations and thus lower friction mobilization and tangential force anisotropy. These findings are relevant to both undrained cyclic deformations of saturated soils and rheology of dense non-Brownian suspensions where volume change is coupled with pore liquid drainage conditions.

Accumulated permanent strain and critical dynamic stress of frozen silty clay under cyclic loading

A series of dynamic triaxial experiments have been conducted to study the dynamic properties of the frozen soil from the subgrade along the Qinghai-Tibet Railway. Under long term cyclic loading, the effects of initial stress state and stress level on cumulative permanent strain and critical dynamic stress were studied in the paper. The results indicate that the influence of dynamic amplitude on the curve of cumulative permanent strain versus cyclic loading number is significant. Besides, based on the shakedown concept, curves of cumulative permanent strain versus cyclic loading number under different initial mean stress and deviatoric stress can be separated to three possible categories of plastic shakedown, plastic creep and incremental collapse. In addition, the critical dynamic stress of frozen soil under specific condition is obtained, and the analysis on critical dynamic stress at different stress state is presented. Therefore, this study could provide an innovative approach for permanent deformation behavior analysis. Furthermore, it is important for practical design and evaluation on stability of frozen soil in the subgrade.

Permanent Deformation Characteristics of Coarse Grained Subgrade Soils under Train-Induced Repeated Load

This paper presents the results of a laboratory experiment that aimed to characterize the permanent deformation behavior of coarse grained soils. To evaluate the effects of the cyclic stress amplitude, initial mean stress, and initial stress ratio on the permanent axial deformation, six series of repeated load triaxial tests were performed. The results indicate that permanent deformation of coarse grained soils increased with increasing cyclic stress amplitude. In particular, for relative low cyclic stress levels, accumulation rate of permanent deformation decreased progressively with number of cycles and eventually reached an equilibrium state. The initial stress ratio was also found to obviously facilitate the buildup of axial deformation since it means higher deviatoric stress as the mean pressure kept constant. As the initial stress ratio was less than the slope of static failure line, the experimental results indicated that the increase of initial mean stress enhanced the capability of resisting deformation. A simplified mechanistic empirical prediction model was proposed, which predicted the permanent deformation as product of four independent functions about cyclic stress amplitude, initial mean stress, initial stress ratio, and number of load cycles. Satisfactory predictions of the permanent deformation behavior of coarse grained soils were obtained with the proposed model.

Elasto-plastic behaviour of frozen soil subjected to long-term low-level repeated loading, Part I: Experimental investigation

The elasto-plastic behaviour of frozen soil subjected to long-term low-level repeated loading is frequently characterized by resilient modulus and accumulated strain, which are significant factors for construction in cold regions. This paper presents an experimental investigation and test results in which accumulated behaviour, including the amount and direction of accumulated strain, is shown to be significantly affected by the initial stress state, repeated stress amplitude and frozen soil strength. Variations in the accumulated direction with increasing numbers of repeated loading cycles cannot be neglected. The resilient modulus, including the shear and bulk components, increases with the accumulation of plastic strain and is clearly dependent on the initial mean stress. These innovative discoveries may help elucidate the properties of frozen soil influenced by long-term low-level vibrations. Furthermore, this work will provide important data for the development of a constitutive model of frozen soil under long-term low-level repeated loading.

A critical state model for sands dependent on stress and density

AbstractAn elastoplastic model for sands is presented in this paper, which can describe stress–strain behaviour dependent on mean effective stress level and void ratio. The main features of the proposed model are: (a) a new state parameter, which is dependent on the initial void ratio and initial mean stress, is proposed and applied to the yield function in order to predict the plastic deformation for very loose sands; and (b) another new state parameter, which is used to determine the peak strength and describe the critical state behaviour of sands during shearing, is proposed in order to predict simply negative/positive dilatancy and the hardening/softening behaviour of medium or dense sands. In addition, the proposed model can also predict the stress–strain behaviour of sands under three‐dimensional stress conditions by using a transformed stress tensor instead of ordinary stress tensor. Copyright © 2004 John Wiley &amp; Sons, Ltd.

The Steady State of Sandy Soils

An alternative procedure to evaluate the void ratio of triaxial test samples is introduced. This method is recommended particularly when very loose samples are tested and an important volume change occurring during the saturation process is expected. In addition, using Toyoura sand a comprehensive set of triaxial tests carried out under both undrained and drained conditions of monotonic loading is presented. For the undrained contractive responses, the results showed two stages associated with the steady state. After the peak strength, the deviator stress drops to a minimum value which can be seen as a quasi steady state, thereafter, the strength increases to an ultimate value corresponding to the actual steady state. Undrained dilative responses clearly indicated the existence of an ultimate state developed at large deformations which represents the steady state of deformation. The results indicate that the quasi steady state is slightly affected by the initial mean stress, whereas, the steady state is unaffected by the initial mean stress. Furthermore, the locus of the ultimate states achieved through drained conditions of loading was shown to be coincident with the steady state line evaluated by means of undrained tests. Finally, according to the relative position of the steady state line with respect to the isotropic consolidation curves for the loosest and densest states of a given soil, the index, Relative Contractiveness, R c , is proposed. It is postulated that R c is related to the inherent liquefaction vulnerability of a soil.

Physical modeling in sand

Small-scale testing under 1 g conditions as well as in the centrifuge presupposes that a model and prototype have comparative behavior. The chief condition for agreement between model and prototype is that the initial soil states of both must be at equal proximity to the steady state line. Then, when stresses are normalized to the initial mean stress, the model will in all aspects behave similarly to the prototype. Scaling rules are presented that indicate the relations between stress, strain, and displacement for the model and the prototype in terms of geometric scale and stress scale. An obvious limit of scales is imposed by that the soil in the model can be no looser than the maximum void ratio. Similarly, it must not be denser than a value that corresponds to a prototype soil at the minimum void ratio. Three main areas of application of the approach in engineering practice are identified: design of representative 1 g small-scale model tests; reanalysis of data from conventional small-scale tests; and improving the versatility of centrifuge facilities in recognition of the fact that the centrifuge test does not need to be performed at equal levels of stress, when designed according to the new approach. Key words : physical modeling, sand, scaling relations, steady state, centrifuge testing.

Exact formulae for stresses around circular holes and inclusions

When a set of loads is applied to an infinite plate containing a circular hole, the stresses around the circumference of the hole are directly related to the stresses around the circumference of the circle in a plate without a hole according to σ θ = 2[ σ i θ − σ i r + σ i o], where σ i o is the initial mean stress at the centre of the circle. No knowledge of the initial shear stresses is required. Related results are given for frictionless and bonded rigid inclusions.